Clement of Rome wrote and epistle to the church at Corinth between a.d. 80 and 100 because the younger generation ousted the established leadership. In the course of his epistle he mentioned the kingdom twice:

1 Clement 42
The apostles received the gospel for us from the Lord Jesus Christ…Having therefore received their orders and being fully assured by the resurrection of our Lord Jesus Christ and full of faith in the word of God, they went forth with the firm assurance that the Holy Spirit gives, preaching the good news that the kingdom of God was about to come. So, preaching both in the country and in the towns, they appointed their first fruits, when they had tested them by the spirit, to be bishops and deacons for the future believers.

1 Clement 50
…All the generations from Adam to this day have passed away, but those who by God’s grace were perfected in love have a place among the godly, who will be revealed when the kingdom of Christ visits us. for it is written: “Enter into the innermost rooms for a very little while, until my anger and wrath shall pass away, and I will remember a good day and will raise you from your graves.”…

The first of these quotes shows that Clement recognized Christ’s disciples performed the same ministry as Jesus. Mark described Jesus’ own gospel message with the following words:

Mark 1.14-15
14 Now after John was arrested, Jesus came into Galilee, proclaiming the gospel of God, 15 and saying, “The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel.”

It is hard to miss the continuity between how Clement describes the disciples and what Mark said about Jesus himself. They both preached the kingdom as gospel. Furthermore we can also observe that Clement does not believe the kingdom came during Jesus’ ministry or even on the day of Pentecost. The disciples carried on the ministry of preaching the kingdom gospel right up until the time when they appointed overseers in the various churches that were present in Clement’s time.

The second text attests not to the proclamation of the kingdom message but to Clement’s own expectation. He looks for the time “when the kingdom of Christ visits us.” Thus, for Clement, the kingdom was undoubtedly a future expectation.